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Cyclist A travelled 60 km. Cyclist B travels 5 km/hr faster than A
and travels the same distance in 2 hours less. Find the speed of each.
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The solution by @Alan is incorrect.
I came to bring you a correct solution.
Let x be the speed of cyclist A, in km/h.
Then the speed of cyclist B is (x+5) km/h, according to the condition.
Cyclist A spent hours.
Cyclist B spent hours.
The difference of times is 2 hours. It gives you THIS "time equation"
- = 2. (1)
At this point, I just can to guess the answer mentally : it is x= 10 km/h.
But let's get it formally . . .
From the time equation, by multiplying both sides by x*(x+5) you get
60(x+5) - 60x = 2x*(x+5)
60x + 300 - 60x = 2x^2 + 10x
300 = 2x^2 + 10x
2x^2 + 10x - 300 = 0
x^2 + 5x - 150 = 0
Factor left side
(x-10)*(x+15) = 0
The last equation has two roots, 10 and -15, of which we select the positive value x= 10.
ANSWER. Cyclists A speed is 10 km/h; Cyclist B speed is 10+5 = 15 km/h.
CHECK. Calculate left side of the equation (1). It is - = 6 - 4 = 2 hours. ! Correct !
Solved.
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Couple of words as a conclusion.
What I presented here, is a standard version and a standard way solving such problems using "time equation".
It is straightforward and clear. It prevents you of making mistakes.
If you deviate from this scheme of writing the solution, and will write a mess, then NOTHING will prevent you
of making mistakes on the way.